Strong Local Non-Determinism of Sub-Fractional Brownian Motion

Let be a subfractional Brownian motion in . We prove that is strongly locally nondeterministic.

Mixed Sub-fractional Brownian Motion and Drift Estimation of Related Ornstein-Uhlenbeck Process

In this paper,wewill first give the numerical simulation of the sub-fractional Brownian motion through the relation of fractional Brownian motion instead of its representation of random walk.In order to verify the rationality of this simulation,we propose a practical estimator associated with the LSE of the drift parameter of mixed sub-fractional Ornstein-Uhlenbeck process,and illustrate the asymptotical properties according to our method of simulation when the Hurst parameter H>1/2.

Influence of Brownian Motion, Thermophoresis and Magnetic Effects on a Fluid Containing Nanoparticles Flowing over a Stretchable Cylinder

The influence of Brownian motion and thermophoresis on a fluid containing nanoparticles flowing over a stretchable cylinder is examined.The classical Navier-Stokes equations are considered in a porous frame.In addition,the Lorentz force is taken into account.The controlling coupled nonlinear partial differential equations are transformed into a system of first order ordinary differential equations by means of a similarity transformation.The resulting system of equations is solved by employing a shooting approach properly implemented in MATLAB.The evolution of the boundary layer and the growing velocity is shown graphically together with the related profiles of concentration and temperature.The magnetic field has a different influence(in terms of trends)on velocity and concentration.

On a Compound Poisson Risk Model Perturbed by Brownian Motion with Variable Premium and Tail Dependence between Claims Amounts and Inter-Claim Time

This paper considers the compound Poisson risk model perturbed by Brownian motion with variable premium and dependence between claims amounts and inter-claim times via Spearman copula. It is assumed that the insurance company’s portfolio is governed by two classes of policyholders. On the one hand, the first class where the amount of claims is high, and on the other hand, the second class where the amount of claims is low, this difference in claim amounts has significant implications for the insurance company’s pricing and risk management strategies. When policyholders are in the first class, they pay an insurance premium of a constant amount c1 and when they are in the second class, the premium paid is a constant amount c2 such that c1 > c2. The nature of claims (low or high) is measured via random thresholds . The study in this work will focus on the determination of the integro-differential equations satisfied by Gerber-Shiu functions and their Laplace transforms in the risk model perturbed by Brownian motion with variable premium and dependence between claims amounts and inter-claim times via Spearman copula. .

The generalized Bouleau-Yor identity for a sub-fractional Brownian motion

Let SH be a sub-fractional Brownian motion with index 0 < H < 1/2.In this paper we study the existence of the generalized quadratic covariation [f(SH),SH](W) defned by[f(SH), SH](W)t= limε→01/ε2H∫t0{f(SHs+ε)-f(SHs)}(SHs+ε-SHs)ds2H,provided the limit exists in probability, where x → f(x) is a measurable function. We construct a Banach space ■ of measurable functions such that the generalized quadratic covariation exists in L2 provided f ∈ H.Moreover, the generalized Bouleau-Yor identity takes the form ∫Rf(x)ψH(dx, t) =(2-22H-1)[f(SH), SH](W)t for all f∈■, where ψH(x, t) is the weighted local time of SH. This allows us to write the generalized It's formula for absolutely continuous functions with derivative belonging to

HARNACK TYPE INEQUALITIES FOR SDES DRIVEN BY FRACTIONAL BROWNIAN MOTION WITH MARKOVIAN SWITCHING

In this paper, by constructing a coupling equation, we establish the Harnack type inequalities for stochastic differential equations driven by fractional Brownian motion with Markovian switching. The Hurst parameter H is supposed to be in(1/2, 1). As a direct application, the strong Feller property is presented.

从x出发的漂移Brownian Motion的极值分布

该文研究了从x出发的正漂移Brownian Motion的极值问题,给出了关于这种随机过程的两种极大值的定义,并主要利用Brownian Motion的一些重要性质,比如正交不变性、时空齐次性及在有限停时上的强Markov性等,获得了两种极大值的分布函数的精确表达式.

LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION

In this article, we study a least squares estimator(LSE) of θ for the OrnsteinUhlenbeck process X_0=0, dX_t =θX_tdt + dB_t^(a,b), t≥ 0 driven by weighted fractional Brownian motion B^(a,b) with parameters a, b. We obtain the consistency and the asymptotic distribution of the LSE based on the observation {X_s, s ∈ [0, t]} as t tends to infinity.

SOME CENTRAL LIMIT THEOREMS FOR SUPER BROWNIAN MOTION

The author proves a central limit theorem for the critical super Brownian motion, which leads to a Gaussian random field. In the transient case the limiting field is the same as that obtained by Dawson (1977). In the recurrent case it is a spatially uniform field. The author also give a central limit theorem for the weighted occupation time of the super Brownian motion with underlying dimension number d < 3, completing the results of Iscoe (1986).

Brownian Motion and the Temperament of Living Cells

The migration of living cells usually obeys the laws of Brownian motion.While the latter is due to the thermal motion of the surrounding matter,the locomotion of cells is generally associated with their vitality.We study what drives cell migration and how to model memory effects in the Brownian motion of cells.The concept of temperament is introduced as an effective biophysical parameter driving the motion of living biological entities in analogy with the physical parameter of temperature,which dictates the movement of lifeless physical objects.The locomemory of cells is also studied via the generalized Langevin equation.We explore the possibility of describing cell locomemory via the Brownian self-similarity concept.An heuristic expression for the diffusion coefficient of cells on structured surfaces is derived.

Some It Formulas with Respect to Mixed Fractional Brownian Motion and Brownian Motion

Some It formulas with respect to mixed Fractional Brownian motion and Brownian motion were given in this paper.These extended the It formula for the fractional Wick It Skorohod integral with respect to Fractional Brownian motion,meanwhile extended the It formula for It Skorohod integral with respect to Brownian motion.Taylor's formula is applied to prove our conclusion in this article.

A LIMINF RESULT FOR HANSON-RUSSO TYPE INCREMENTS OF FRACTIONAL BROWNIAN MOTION

Let {X(t), t > 0} be a fractional Brownian motion of order 2α with 0 < α <1,β > 0 be a real number, aT be a function of T and 0 < aT< T, lim(log T/aT)/log log T = r, (0 < r<∞). In this paper, we proved thatwhere c1, c2 are two positive constants depending only on α,β.

Thermophoresis and Brownian motion effects on boundary layer flow of nanofluid in presence of thermal stratification due to solar energy

The problem of laminar fluid flow,which results from the stretching of a vertical surface with variable stream conditions in a nanofluid due to solar energy,is investigated numerically.The model used for the nanofluid incorporates the effects of the Brownian motion and thermophoresis in the presence of thermal stratification.The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations,namely,the scaling group of transformations.An exact solution is obtained for the translation symmetrys,and the numerical solutions are obtained for the scaling symmetry.This solution depends on the Lewis number,the Brownian motion parameter,the thermal stratification parameter,and the thermophoretic parameter.The conclusion is drawn that the flow field,the temperature,and the nanoparticle volume fraction profiles are significantly influenced by these parameters.Nanofluids have been shown to increase the thermal conductivity and convective heat transfer performance of base liquids.Nanoparticles in the base fluids also offer the potential in improving the radiative properties of the liquids,leading to an increase in the efficiency of direct absorption solar collectors.

On p-variation of bifractional Brownian motion

In this paper we study p-variation of bifractional Brownian motion. As an applica-tion, we introduce a class of estimators of the parameters of a bifractional Brownian motion andprove that both of them are strongly consistent; as another application, we investigate fractalnature related to the box dimension of the graph of bifractional Brownian motion.

On the sub-mixed fractional Brownian motion

Let {SHt, t ≥ 0} be a linear combination of a Brownian motion and an independent sub-fractional Brownian motion with Hurst index 0 < H < 1. Its main properties are studied.They suggest that SHlies between the sub-fractional Brownian motion and the mixed fractional Brownian motion. We also determine the values of H for which SHis not a semi-martingale.

On the Reflected Geometric Brownian Motion with Two Barriers

In this paper, we are concerned with Re?ected Geometric Brownian Motion (RGBM) with two barriers. And the stationary distribution of RGBM is derived by Markovian in?nitesimal Generator method. Consequently the ?rst passage time of RGBM is also discussed.

POWER VARIATION OF SUBFRACTIONAL BROWNIAN MOTION AND APPLICATION

In this paper,we consider the power variation of subfractional Brownian motion.As an application,we introduce a class of estimators for the index of a subfractional Brownian motion and show that they are strongly consistent.

The Arc-Sine Laws for the Skew Brownian Motion and Their Interpretation

We consider the skew Brownian motion as a solution of some stochastic differential equation. We prove for the skew Brownian motion the analogues of the arc-sine laws for Wiener process. Unlike of existing results, we are forced to consider a stochastic differential equation with discontinuous diffusion coefficient. Possible interpretations of obtained results are suggested.

An image encryption scheme based on three-dimensional Brownian motion and chaotic system

At present, many chaos-based image encryption algorithms have proved to be unsafe, few encryption schemes permute the plain images as three-dimensional(3D) bit matrices, and thus bits cannot move to any position, the movement range of bits are limited, and based on them, in this paper we present a novel image encryption algorithm based on 3D Brownian motion and chaotic systems. The architecture of confusion and diffusion is adopted. Firstly, the plain image is converted into a 3D bit matrix and split into sub blocks. Secondly, block confusion based on 3D Brownian motion(BCB3DBM)is proposed to permute the position of the bits within the sub blocks, and the direction of particle movement is generated by logistic-tent system(LTS). Furthermore, block confusion based on position sequence group(BCBPSG) is introduced, a four-order memristive chaotic system is utilized to give random chaotic sequences, and the chaotic sequences are sorted and a position sequence group is chosen based on the plain image, then the sub blocks are confused. The proposed confusion strategy can change the positions of the bits and modify their weights, and effectively improve the statistical performance of the algorithm. Finally, a pixel level confusion is employed to enhance the encryption effect. The initial values and parameters of chaotic systems are produced by the SHA 256 hash function of the plain image. Simulation results and security analyses illustrate that our algorithm has excellent encryption performance in terms of security and speed.

Brownian Motion of Decaying Particles: Transition Probability, Computer Simulation, and First-Passage Times

Recent developments in the measurement of radioactive gases in passive diffusion motivate the analysis of Brownian motion of decaying particles, a subject that has received little previous attention. This paper reports the derivation and solution of equations comparable to the Fokker-Planck and Langevin equations for one-dimensional diffusion and decay of unstable particles. In marked contrast to the case of stable particles, the two equations are not equivalent, but provide different information regarding the same stochastic process. The differences arise because Brownian motion with particle decay is not a continuous process. The discontinuity is readily apparent in the computer-simulated trajectories of the Langevin equation that incorporate both a Wiener process for displacement fluctuations and a Bernoulli process for random decay. This paper also reports the derivation of the mean time of first passage of the decaying particle to absorbing boundaries. Here, too, particle decay can lead to an outcome markedly different from that for stable particles. In particular, the first-passage time of the decaying particle is always finite, whereas the time for a stable particle to reach a single absorbing boundary is theoretically infinite due to the heavy tail of the inverse Gaussian density. The methodology developed in this paper should prove useful in the investigation of radioactive gases, aerosols of radioactive atoms, dust particles to which adhere radioactive ions, as well as diffusing gases and liquids of unstable molecules.