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small typo on the Hawkes definition #6

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small typo on the Hawkes definition #6

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3 changes: 2 additions & 1 deletion 2026 Video Lectures/94. Hawkes Processes for Quant Finance/hpqf.ipynb
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Expand Up @@ -931,6 +931,7 @@
" \\lambda(t) = \\mu + \\sum_{t_i < t} \\phi(t - t_i)\n",
" $$\n",
" \n",
" - $\\t_i$: time of previous events that occures\n",
" - $\\mu$: baseline (exogenous) event rate.\n",
" - $\\phi(t - t_i)$: triggering kernel measuring the influence of past event at $t_i$ on the current intensity.\n",
" \n",
Expand Down Expand Up @@ -1102,7 +1103,7 @@
"The counting process $N(t)$ then follows:\n",
"\n",
"$$\n",
"N(t) \\sim \\text{Hawkes}\\left(\\lambda(s) \\text{ as above}\\right)\n",
"N(t) \\sim \\text{Poisson}\\left(\\lambda(t) \\text{ as above}\\right)\n",
"$$\n",
"\n",
"*Like the inhomogeneous Poisson process, increments are independent given the path of $\\lambda(t)$, but here $\\lambda(t)$ depends on the process history.*"
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