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We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the periodicity for the solution. In particular, we found…
The technique of stochastic solutions, previously used for deterministic equations, is here proposed as a solution method for partial differential equations driven by distribution-valued noises.
We study a kind of better recurrence than Kolmogorov's one: periodicity recurrence,which corresponds periodic solutions in distribution for stochastic differential equations. On the basis of technique of upper and lower solutions and…
In this paper we study the randomized non-autonomous complete linear differential equation. The diffusion coefficient and the source term in the differential equation are assumed to be stochastic processes and the initial condition is…
We investigate the periodic and stationary solutions of distribution-dependent stochastic differential equations. While generally, the semigroups associated with the equations are nonlinear, we show that the methods of weak convergence and…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
In this paper, we discuss the relationships between stability and almost periodicity for solutions of stochastic differential equations. Our essential idea is to get stability of solutions or systems by some inherited properties of Lyapunov…
Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…
In this paper, we introduce concepts of pathwise random almost periodic and almost automorphic solutions for dynamical systems generated by non-autonomous stochastic equations. These solutions are pathwise stochastic analogues of…
In this paper, random and stochastic processes are defined on fractal curves. Fractal calculus is used to define cumulative distribution function, probability density function, moments, variance and correlation function of stochastic…
In this paper we study the randomized heat equation with homogeneous boundary conditions. The diffusion coeffcient is assumed to be a random variable and the initial condition is treated as a stochastic process. The solution of this…
A method for the construction of approximate analytical expressions for the stationary marginal densities of general stochastic search processes is proposed. By the marginal densities, regions of the search space that with high probability…
This paper establishes an existence theory for distributed periodic solutions to Newton's equation with stochastic time-periodic forcing, where the friction matrix is the Hessian of a twice continuously differentiable friction function.…
In this paper, we study the existence and uniqueness of periodic solutions of the differential equation of the form . Here, we obtain some sufficient conditions which guarantee the existence of periodic solutions. This equation is a quite…
We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation…
In this paper, we prove the existence of periodic solutions for McKean-Vlasov SDEs under periodic distribution-dependent Lyapunov conditions, which is obtained by periodic Markov processes with state space $\mathbb R^d\times \mathcal…
We tackle the problem of conditioning probabilistic programs on distributions of observable variables. Probabilistic programs are usually conditioned on samples from the joint data distribution, which we refer to as deterministic…
In this paper we give stochastic solutions of conformable fractional Cauchy problems. The stochastic solutions are obtained by running the processes corresponding to Cauchy problems with a nonlinear deterministic clock.
This paper is concerned with the existence and uniqueness of random periodic solutions for stochastic differential equations (SDEs), where the drift terms involved need not to be uniformly dissipative. On the one hand, via the reflection…
Statistical systems with time-periodic spatially non-uniform forces are of immense importance in several areas of physics. In this paper, we provide an analytical expression of the time-periodic probability distribution function of…