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Lower error bounds and optimality of approximation for jump-diffusion SDEs with discontinuous drift. [PDF]
BIT Numer MathPrzybyłowicz P +2 more
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Evolution's hidden architecture: a non-lipschitz theory of creation and catastrophe. [PDF]
BMC Ecol EvolDurán-Olivencia MA.
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Partial differential equations in data science. [PDF]
Philos Trans A Math Phys Eng SciBertozzi AL +3 more
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On Differential Equations with Codimension-$n$ Discontinuity Sets
SIAM Journal on Applied Dynamical Systems, 2021The paper is focused on a class of vector fields including Filippov systems and extended Filippov systems which are smooth everywhere except in a codimension-\(n\) submanifold of the phase space. The authors use a basic approach of polar blow-up around the codimension-\(n\) discontinuity set for the investigation of the local dynamics of the vector ...
Peter L. Varkonyi, Mate Antali
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A Unified Variational Approach to Discontinuous Differential Equations
Mediterranean Journal of Mathematics, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Radu Precup, Jorge Rodríguez-López
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On differential algebraic equations with discontinuities
ZAMP Zeitschrift f�r angewandte Mathematik und Physik, 1992Many of the differential algebraic equations (DAEs) that arise in control problems take the form \(A(z,u)z'=f_ 1(z,u)\), \(0=f_ 2(z,u)\), \(z(0)=z_ 0\) where \(A\) is singular but has constant rank. This paper examines what the response of the state should be if the control \(u\) has a jump discontinuity at a time \(t_ 0\).
Brüll, L., Pallaske, U.
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Stochastic differential equations with discontinuous diffusion coefficients
Theory of Probability and Mathematical Statistics, 2023We study one-dimensional stochastic differential equations of the form d X t = σ ( X t ) d Y t dX_t = \sigma (X_t)dY_t , where Y Y is a suitable Hölder continuous driver such as the ...
Torres, Soledad, Viitasaari, Lauri
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On discontinuously perturbed carathéodory type differential equations
Nonlinear Analysis: Theory, Methods & Applications, 1996The solvability of the initial value problem \((*)\) \(x' = q(x) g(t,x)\), \(x(0) = x_0\) is studied. Here \((t,x) \in [0,T] \times R\), the positive measurable function \(q(x)\) is locally bounded, and \(q^{-1} (x)\) is locally essentially bounded; the Carathéodory function \(g(t,x)\) satisfies some additional growth conditions.
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