On a class of forward-backward stochastic differential systems in infinite dimensions.
On a class of measure-dependent stochastic evolution equations driven by fbm.
On a Class of Nonlinear Stochastic Evolution Equations.
On a SDE driven by a fractional Brownian motion and with monotone drift.
On a simulation of the oscillation excited by a random force
On a stochastic SIR model
We consider a stochastic SIR system and we prove the existence, uniqueness and positivity of solution. Moreover the existence of an invariant measure under a suitable condition on the coefficients is studied.
On almost sure convergence of modified Euler-Peano approximation of solution to an S.D.E. driven by a semimartingale
On approximate large deviations for 1D diffusion.
On approximation of solutions to a class of stochastic equations.
On changes of measure in stochastic volatility models.
On differential equations and inclusions with mean derivatives on a compact manifold
We introduce and investigate a new sort of stochastic differential inclusions on manifolds, given in terms of mean derivatives of a stochastic process, introduced by Nelson for the needs of the so called stochastic mechanics. This class of stochastic inclusions is ideologically the closest one to ordinary differential inclusions. For inclusions with forward mean derivatives on manifolds we prove some results on the existence of solutions.
On equivalence of a class of random processes in Hilbert space and a Wiener process.
On equivalence of a process of diffusion type in Hilbert space and a Wiener process.
On European option pricing under partial information
We consider a European option pricing problem under a partial information market, i.e., only the security's price can be observed, the rate of return and the noise source in the market cannot be observed. To make the problem tractable, we focus on gap option which is a generalized form of the classical European option. By using the stochastic analysis and filtering technique, we derive a Black-Scholes formula for gap option pricing with dividends under partial information. Finally, we apply filtering...
On generalized probabilistic 2-normed spaces.
On invariant measures of nonlinear Markov processes.
On least squares estimation in continuous time linear stochastic systems
On Lipschitz Dependence in Systems with Differentiated Inputs.
On near-optimal necessary and sufficient conditions for forward-backward stochastic systems with jumps, with applications to finance
We establish necessary and sufficient conditions of near-optimality for nonlinear systems governed by forward-backward stochastic differential equations with controlled jump processes (FBSDEJs in short). The set of controls under consideration is necessarily convex. The proof of our result is based on Ekeland's variational principle and continuity in some sense of the state and adjoint processes with respect to the control variable. We prove that under an additional hypothesis, the near-maximum...
On Newton's method for stochastic differential equations