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We study parameter estimation problem for diagonalizable parabolic stochastic partial differential equations driven by a multiplicative fractional noise with any Hurst parameter H 2 (0, 1). Two clas...
In this paper we derive lower bounds in minimax sense for estimation of the instantaneous volatility if the diffusion type part cannot be observed directly but under some additional Gaussian noise. ...
The basic model for high-frequency data in finance is considered, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam’s se...
We consider the problem of estimating a deterministic sparse vector x0 from underdetermined measurements Ax0 + w, where w represents white Gaussian noise and A is a given deterministic dictionary. ...
The control process that minimizes the quadratic performance functional associated with a quantum system whose evolution is described by a Hudson-Parthasarathy type stochastic differential equation...
We prove the existence and uniqueness theorem for stochastic differential equation8 with bounded coefficients driven by the renormalized square of white noise. These equations are interpreted as se...
We generalize the result of Komorowski and Papanicolaou published in [I.W e consider the solution of stochastic differentid equation dX(t) = V(t, x (t)) dt + (t), where E (2) is a standard d-dimens...
We introduce dzerent ways of being dependent for the input noise of stochastic algorithms. We are aimed to prove that such innovations allow to use the ODE (ordinary differential equation) method. ...
A Non-Linear Eroder in Presence of One-Sided Noise
We consider a semiparametric convolution model. We observe random variables having a distribution given by the convolution of some unknown density $f$ and some partially known noise density $g$. In th...
We consider a system of d coupled non-linear stochastic heat equations in spatial dimension 1 driven by d-dimensional additive space-time whitenoise. We establish upper and lower bounds on hitting pro...
In this paper we derive tight bounds on the expected value of products of low influence functions defined on correlated probability spaces. The proofs are based on extending Fourier theory to an arbit...
This paper concerns the Markov process duality between the one-dimensional heat equation driven by Fisher-Wright white noise and slowly coalescing Brownian particles. A representation is found for the...

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