Feller property of regime-switching jump diffusion processes with hybrid jumps

Figures & data

Table 1. Conditions imposed by [22–27] on key elements in (1.1(1.1) $$\begin{array}{ll}d{X}_t& =a(X_t,{\theta }_t)dt+b(X_t,{\theta }_t)d{W}_t+\underset{V}{\int }{g}_1(X_{t-},{\theta }_{t-},v)q_1(dt,dv)\\ & +\underset{U}{\int }{g}_2(X_{t-},{\theta }_{t-},u)p_2(dt,du)\end{array}$$(1.1) )-(1.2(1.2) $$\begin{array}{ll}d{\theta }_t& =\underset{U}{\int }c(X_{t-},{\theta }_{t-},u)p_2(dt,du)\end{array}$$(1.2) ) for the Feller property.

Source	𝕄	Πij(x)	V	$g_1(x,.,.)$	U	$c(x,.,.)$	$g_2(x,.,.)$
[22]	Finite	Continuous	-	= 0	ℝ	Measurable	= 0
[23]	Countable	Lipschitz	-	= 0	ℝ	Measurable	= 0
[24]	Countable	Continuous	-	= 0	ℝ	Measurable	= 0
[25], [26]	Countable	Lipschitz	ℝ	Locally Lipschitz	ℝ	Measurable	= 0
[27]	Finite	Lipschitz	ℝ	Locally Lipschitz	ℝ	Measurable	Bounded

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