On solutions of general nonlinear stochastic integral equations.
On solutions set of a multivalued stochastic differential equation
We analyse multivalued stochastic differential equations driven by semimartingales. Such equations are understood as the corresponding multivalued stochastic integral equations. Under suitable conditions, it is shown that the considered multivalued stochastic differential equation admits at least one solution. Then we prove that the set of all solutions is closed and bounded.
On some fractional stochastic integrodifferential equations in Hilbert space.
On some limit theorems for solutions of stochastic differential equations
On some sample path properties of Skorohod integral processes
On Stochastic Differential Equations with Reflecting Boundary Condition in Convex Domains
Let D be an open convex set in and let F be a Lipschitz operator defined on the space of adapted càdlàg processes. We show that for any adapted process H and any semimartingale Z there exists a unique strong solution of the following stochastic differential equation (SDE) with reflection on the boundary of D: , t ∈ ℝ⁺. Our proofs are based on new a priori estimates for solutions of the deterministic Skorokhod problem.
On the existence and asymptotic behavior of the random solutions of the random integral equation with advancing argument
1. Introduction Random Integral Equations play a significant role in characterizing of many biological and engineering problems [4,5,6,7]. We present here new existence theorems for a class of integral equations with advancing argument. Our method is based on the notion of a measure of noncompactness in Banach spaces and the fixed point theorem of Darbo type. We shall deal with random integral equation with advancing argument , (t,ω) ∈ R⁺ × Ω, (1) where (i) (Ω,A,P) is a complete probability space, (ii)...
On the existence and uniqueness of the solution processes in McShane's stochastic integral equation systems
On the existence, uniqueness and parametric dependence on the coefficients of the solution processes in McShane's stochastic integral equations.
In this paper we use the Schauder fixed point theorem and methods of integral inequalities in order to prove a result on the existence, uniqueness and parametric dependence on the coefficients of the solution processes in McShane stochastic integral equations.
On the positivity and zero crossings of solutions of stochastic Volterra integrodifferential equations.
On the probability model for solving some integral equations of second type
On the uniqueness of solutions of stochastic differential equations with reflecting barrier conditions
Onsager-Machlup functional for stochastic evolution equations
Parametric dependence of the solution processes on the coefficients in McShane's stochastic integral equation systems
Pathwise differentiability with respect to a parameter of solutions of stochastic differential equations
Path-wise solutions of stochastic differential equations driven by Lévy processes.
In this paper we show that a path-wise solution to the following integral equationYt = ∫0t f(Yt) dXt, Y0 = a ∈ Rd,exists under the assumption that Xt is a Lévy process of finite p-variation for some p ≥ 1 and that f is an α-Lipschitz function for some α > p. We examine two types of solution, determined by the solution's behaviour at jump times of the process X, one we call geometric, the other forward. The geometric solution is obtained by adding fictitious time and solving an associated...
Penalisations of multidimensional Brownian motion, VI
As in preceding papers in which we studied the limits of penalized 1-dimensional Wiener measures with certain functionals Γt, we obtain here the existence of the limit, as t → ∞, of d-dimensional Wiener measures penalized by a function of the maximum up to time t of the Brownian winding process (for d = 2), or in {d}≥ 2 dimensions for Brownian motion prevented to exit a cone before time t. Various extensions of these multidimensional penalisations are studied, and the limit laws are described....
Periodic and almost periodic flows of periodic Ito equations
Under the uniform asymptotic stability of a finite dimensional Ito equation with periodic coefficients, the asymptotically almost periodicity of the -bounded solution and the existence of a trajectory of an almost periodic flow defined on the space of all probability measures are established.
Processus associés à l'équation des milieux poreux
Proof(s) of the Lamperti representation of continuous-state branching processes.