Some remarks on single jump processes
Some remarks on the theory of stochastic integration
Stability of stochastic processes defined by integral functionals
The paper is devoted to the study of integral functionals for continuous nonincreasing functions f and nonnegative stochastic processes X(t,ω) with stationary and independent increments. In particular, a concept of stability defined in terms of the functionals with a ∈ (0,∞) is discussed.
Stable convergence of generalized stochastic integrals and the principle of conditioning.
Stationary Quantum Markov processes as solutions of stochastic differential equations
From the operator algebraic approach to stationary (quantum) Markov processes there has emerged an axiomatic definition of quantum white noise. The role of Brownian motion is played by an additive cocycle with respect to its time evolution. In this report we describe some recent work, showing that this general structure already allows a rich theory of stochastic integration and stochastic differential equations. In particular, if a quantum Markov process is represented by a unitary cocycle, we can...
Stochastic analysis and local times for (N, d)-Wiener process
Stochastic calculus and the continuity of local times of Lévy processes
Stochastic calculus, statistical asymptotics, Taylor strings and phyla
Stochastic calculus with respect to fractional Brownian motion
Fractional Brownian motion (fBm) is a centered self-similar Gaussian process with stationary increments, which depends on a parameter called the Hurst index. In this conference we will survey some recent advances in the stochastic calculus with respect to fBm. In the particular case , the process is an ordinary Brownian motion, but otherwise it is not a semimartingale and Itô calculus cannot be used. Different approaches have been introduced to construct stochastic integrals with respect to fBm:...
Stochastic evolution equations driven by Liouville fractional Brownian motion
Let be a Hilbert space and a Banach space. We set up a theory of stochastic integration of -valued functions with respect to -cylindrical Liouville fractional Brownian motion with arbitrary Hurst parameter . For we show that a function is stochastically integrable with respect to an -cylindrical Liouville fractional Brownian motion if and only if it is stochastically integrable with respect to an -cylindrical fractional Brownian motion. We apply our results to stochastic evolution equations...
Stochastic fuzzy differential equations with an application
In this paper we present the existence and uniqueness of solutions to the stochastic fuzzy differential equations driven by Brownian motion. The continuous dependence on initial condition and stability properties are also established. As an example of application we use some stochastic fuzzy differential equation in a model of population dynamics.
Stochastic heat equation with white-noise drift
Stochastic Holomorphy.
Stochastic integral by a semi-Markov process of diffusion type.
Stochastic integral equations for the random fields
Stochastic integral of divergence type with respect to fractional brownian motion with Hurst parameter
Stochastic integrals and progressive measurability. An example
Stochastic integration in abstract spaces.
Stochastic integration of functions with values in a Banach space
Let H be a separable real Hilbert space and let E be a real Banach space. In this paper we construct a stochastic integral for certain operator-valued functions Φ: (0,T) → ℒ(H,E) with respect to a cylindrical Wiener process . The construction of the integral is given by a series expansion in terms of the stochastic integrals for certain E-valued functions. As a substitute for the Itô isometry we show that the square expectation of the integral equals the radonifying norm of an operator which is...
Stochastic integration on nuclear spaces and its applications